This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A377234 #15 May 04 2025 04:23:32
%S A377234 1,12,138,1524,16455,175152,1846164,19320456,201093843,2084105820,
%T A377234 21524823858,221678089716,2277558628869,23352604052952,
%U A377234 239024756624520,2442818071519104,24932208295715538,254166614639215032,2588333499216072516,26333774228774140680,267693203735009601870
%N A377234 Expansion of 1/(1 - 9*x/(1-x))^(4/3).
%F A377234 a(0) = 1; a(n) = 3 * Sum_{k=0..n-1} (4-k/n) * a(k).
%F A377234 a(n) = ((11*n+1)*a(n-1) - 10*(n-2)*a(n-2))/n for n > 1.
%F A377234 a(n) = Sum_{k=0..n} (-9)^k * binomial(-4/3,k) * binomial(n-1,n-k).
%F A377234 a(n) ~ 3^(11/3) * 10^(n - 4/3) * n^(1/3) / Gamma(1/3). - _Vaclav Kotesovec_, Oct 21 2024
%F A377234 a(n) = 12*hypergeom([7/3, 1-n], [2], -9) for n > 0. - _Stefano Spezia_, May 04 2025
%o A377234 (PARI) a(n) = sum(k=0, n, (-9)^k*binomial(-4/3, k)*binomial(n-1, n-k));
%Y A377234 Cf. A052268, A361375, A377233, A377235.
%K A377234 nonn
%O A377234 0,2
%A A377234 _Seiichi Manyama_, Oct 21 2024